If $A$, $B$ are two non-singular matrices of order $3$ and $I$ is an identity matrix of order $3$ such that $A{A}^T=5\mathrm{{\rm I}}$ and $3A^{-1}=2A^T-A\mathrm{a}\mathrm{d}\mathrm{j}\left(4B\right)$, then ${\left|B\right|}^2$ is equal to (where $A^T$ and $\mathrm{a}\mathrm{d}\mathrm{j}\left(A\right)$ denote transpose and adjoint matrices of the matrix $A$ respectively)

• Correct answer
  A

  $\frac{7^3}{5^3\cdot 4^6}$
• B

  $\frac{7^3}{5^3\cdot 4^3}$
• C

  $\frac{7^4}{5^3\cdot 2^{12}}$
• D

  $\frac{5^6}{7^3\cdot 2^{10}}$

Hence, the correct answer is option: 'A'.